Adding, Subtracting, Multiplying & Dividing Negative Numbers
Negative numbers follow consistent rules. Once you learn them, they become second nature.
Adding and subtracting
Same signs
Add the numbers and keep the sign.
−5 + (−3) = −8
Different signs
Subtract the smaller from the larger and take the sign of the larger.
5 + (−3) = 2 (5 − 3 = 2, sign of 5 is +)
Subtraction = add the opposite
Subtracting a number is the same as adding its opposite. This simplifies everything.
5 − (−3) = 5 + 3 = 8
−5 − (−3) = −5 + 3 = −2
Key: Two negatives in a row (minus a negative) become a plus.
Multiplying and dividing
The sign rules are the same for both:
- Same signs → positive result
- Different signs → negative result
−4 × (−3) = 12
−4 × 3 = −12
4 × (−3) = −12
−12 ÷ (−4) = 3
−12 ÷ 4 = −3
12 ÷ (−4) = −3
Quick reference
- + + or − − → positive
- + − or − + → negative
- a − (−b) = a + b
Common mistakes
Subtracting a negative: Subtracting a negative is the same as adding. 5 − (−3) = 5 + 3 = 8, not 2.
Multiplying sign rules: Positive × positive = positive. Negative × negative = positive. Positive × negative = negative. The odd one that trips people up: (−2) × (−4) = +8.
Order on the number line: −5 is less than −2 because it's further left on the number line. Don't compare just the digits.
More examples
Example: −8 + 3
Example: (−6) × (−7)
6 × 7 = 42
Answer: +42
Example: −15 ÷ 3
15 ÷ 3 = 5
Answer: −5
Practice problems
1. Solve: −4 + (−6)
Show answer
2. Solve: 3 − (−5)
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3. Solve: (−9) × 4
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Practice these rules in a stress-free way with Arithmia — a cozy math puzzle game.